Bit harsh to condemn a home for a frozen pipe. Still.
Scarlett, are all the hot water taps frozen or just the bath tap? If it is just the bath tap........open it(ie have it turned to water on) Then get someone to follow the pipe back to say a junction and feel if the pipe there is warm. Then from that point use a hair drier to warm the frozen pipe, starting at the end nearest the tap. It is important to have the tap open when you do this to allow any steam or water to escape. Then lag or insulate the tap. As for your kitchen sink waste being frozen. Firstly just check outside where it outfalls into say a drain, if there is a lump of ice at the end of the pipe.....break it off. The sink waste outlet is liable to be plastic so do not overheat it if you use a hair drier. You could try boiling a kettle and pouring it into the sink. If the sink is full of water you will have to empty it with pans or a jug etc. When this cold spell has ended it may be worth getting the pipes lagged . Just a tip if you get the bath tap pipe unfrozen and running again, you may want to leave it just running, no more than a trickle, whilst this cold snap is on. The warm water flowing will prevent further freezing until you can get it lagged.